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    <title>pbig</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>pbig</b> -  eigen-projection</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[Q,M]=pbig(A,thres,flag)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>A</b>
        </tt>: real square matrix</li>
      <li>
        <tt>
          <b>thres</b>
        </tt>: real number</li>
      <li>
        <tt>
          <b>flag</b>
        </tt>: character string (<tt>
          <b>'c'</b>
        </tt> or <tt>
          <b>'d'</b>
        </tt>)</li>
      <li>
        <tt>
          <b>Q,M</b>
        </tt>: real matrices</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Projection on eigen-subspace associated with eigenvalues with real
    part &gt;= <tt>
        <b>thres</b>
      </tt> (<tt>
        <b>flag='c'</b>
      </tt>) or
    with magnitude &gt;= <tt>
        <b>thres</b>
      </tt>
    (<tt>
        <b>flag='d'</b>
      </tt>).</p>
    <p>
    The projection is defined by <tt>
        <b>Q*M</b>
      </tt>, <tt>
        <b>Q</b>
      </tt> is
    full column rank, <tt>
        <b>M</b>
      </tt> is full row rank and
    <tt>
        <b>M*Q=eye</b>
      </tt>.</p>
    <p>
    If <tt>
        <b>flag='c'</b>
      </tt>, the eigenvalues of
    <tt>
        <b>M*A*Q</b>
      </tt> = eigenvalues of <tt>
        <b>A</b>
      </tt> with real part
    &gt;= <tt>
        <b>thres</b>
      </tt>.</p>
    <p>
    If <tt>
        <b>flag='d'</b>
      </tt>, the eigenvalues of
    <tt>
        <b>M*A*Q</b>
      </tt> = eigenvalues of <tt>
        <b>A</b>
      </tt> with magnitude
    &gt;= <tt>
        <b>thres</b>
      </tt>.</p>
    <p>
    If <tt>
        <b>flag='c'</b>
      </tt> and if <tt>
        <b>[Q1,M1]</b>
      </tt> =
    full rank factorization (<tt>
        <b>fullrf</b>
      </tt>) of
    <tt>
        <b>eye()-Q*M</b>
      </tt> then eigenvalues of <tt>
        <b>M1*A*Q1</b>
      </tt> =
    eigenvalues of <tt>
        <b>A</b>
      </tt> with real part &lt;
    <tt>
        <b>thres</b>
      </tt>.</p>
    <p>
    If <tt>
        <b>flag='d'</b>
      </tt> and if <tt>
        <b>[Q1,M1]</b>
      </tt> =
    full rank factorization (<tt>
        <b>fullrf</b>
      </tt>) of
    <tt>
        <b>eye()-Q*M</b>
      </tt> then eigenvalues of <tt>
        <b>M1*A*Q1</b>
      </tt> =
    eigenvalues of <tt>
        <b>A</b>
      </tt> with magnitude &lt;
    <tt>
        <b>thres</b>
      </tt>.</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

A=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
[Q,M]=pbig(A,1.5,'d');
spec(M*A*Q)
[Q1,M1]=fullrf(eye()-Q*M);
spec(M1*A*Q1)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="psmall.htm">
        <tt>
          <b>psmall</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="projspec.htm">
        <tt>
          <b>projspec</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="fullrf.htm">
        <tt>
          <b>fullrf</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="schur.htm">
        <tt>
          <b>schur</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>F. D. (1988); ;   </p>
    <h3>
      <font color="blue">Used Function</font>
    </h3>
    <p>
      <tt>
        <b>pbig</b>
      </tt> is based on the ordered schur form (scilab
   function <tt>
        <b>schur</b>
      </tt>).</p>
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